Reference no: EM131013328
1. Find the minimum and maximum values of the function subject to the constraint.
F(x. y, z) = 3x + 2y + 4z, x2 + 2y2 + = 1
2. Compute the Riemann sum S for the double integral where R = [1, 4] x [1, 3], for the grid and sample points shown in figure below.
3. Evaluate ∫∫R (50 - 10x) dA, where R = [0, 5] x [0, 3].
4. The following table gives the approximate height (in meters) at quarter-meter intervals of a mound of gravel.
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0.75
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0.2
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0.5
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0.5
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0.25
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0.2
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0.5
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0.5
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0.6
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0.8
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0.7
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0.5
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0.25
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0.05
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0.5
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0.7
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0.6
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0.5
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0
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0.2
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0.25
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0.5
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0.25
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0.2
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y/x
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0
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0.25
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0.5
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0.75
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1
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Estimate the volume V of the mound by computing the average of the two Riemann sums4,3 with lower-left and upper-right vertices of the sub rectangles as sample points.
5. Use symmetry to evaluate the double integral.
∫∫R 5 sin dA, R = [0, 2π] x [0, 2π].
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Estimate the volume v of the mound by computing the average
: Estimate the volume V of the mound by computing the average of the two Riemann sums4,3 with lower-left and upper-right vertices of the sub rectangles as sample points.
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